Applications and numerical investigation of differential-algebraic equations

Abstract

Differential-algebraic equations (DAEs) result in many areas of science and engineer- ing. In this thesis, numerical methods for solving DAEs are compared for two prob- lems, energy-economic models and traffic flow models. An energy-economic model is presented based on the Hubbert model of oil production and is extended to include economic factors for the first time. Using numerical methods to simulate the DAE model, the resulting graphs break the symmetry of the traditional Hubbert curve. For the traffic flow models, a numerical method is developed to solve the steady-state flow pattern including the linearly unstable regime, i.e. solutions which cannot be found with an initial value solver.